Respuesta :

Answer:

h'(-1) = 5

Explanation:

Given - The table above gives values of f, f’, g, and g’ at selected values

             of x.

x              f(x)                   f'(x)                    g(x)                      g'(x)

-1              6                      5                         3                          -2

1               3                      -3                        -1                          2

3               1                      -2                         2                          3

To find - If h(x) = f(g(x)), then h’(1) = ......?

Proof -

Given that,

h(x) = f(g(x))

⇒h'(x) = f'(g(x))

⇒h'(1) = f'(g(1))

Now,

g(1) = -1

⇒f'(-1) = 5

⇒h'(-1) = 5

MrRoyal

A composite function combines two or more functions.

The value of h'(1) is 5

The given parameter is:

[tex]\mathbf{h(x) = f(g(x)}}[/tex]

Take inverse of both sides

[tex]\mathbf{h'(x) = f'(g(x)}}[/tex]

Substitute 1 for x

[tex]\mathbf{h'(1) = f'(g(1))}}[/tex]

From the table, we have:

[tex]\mathbf{g(1) = -1}[/tex]

So, the equation becomes

[tex]\mathbf{h'(1) = f'(-1)}}[/tex]

From the table, we have:

[tex]\mathbf{f'(-1) =5}[/tex]

So, the equation becomes

[tex]\mathbf{h'(1) = 5}[/tex]

Hence, the value of h'(1) is 5

Read more about composite functions at:

https://brainly.com/question/18839694

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